On some asymptotical shape problems

Article type: Research Article

Authors: Nayam, Al-hassem

Affiliations: International Centre for Theoretical Physics, Strada Costiera, 11, I-34151 Trieste, Italy. E-mail: [email protected]

Abstract: We consider the problem of the optimal location of a Dirichlet region in a d-dimensional domain Ω subjected to a given force f in order to minimize a given functional. We look for the optimal region among the class of all closed connected sets of assigned total length l. Then we let l tend to infinity and we look at the Γ-limit of a suitable rescaled functional, in order to get information of the asymptotic distribution of the optimal region.

Keywords: optimal network location, shape optimization, Γ-convergence

DOI: 10.3233/ASY-121156

Journal: Asymptotic Analysis, vol. 83, no. 4, pp. 285-302, 2013